Abstract : Generally, the wave-function of twoisolated particles after a mutual interaction cannot be expressedas a product of the particles' individual states. However,maximal entanglement is produced in an atomic collisiononly under exceptional conditions. These conditions are met in ourset-up, where the dipole-dipole interaction between 'two level'Rydberg atoms can be stimulated by a non-resonant superconductingcavity. By exploiting this effect, we have realised stronglyentangled states in a collision with an impact parameter in themillimeter range. The collision mixing angle can be modified bychanging the atoms-cavity detuning. We have thus observedreversible and coherent energy exchange (Rabi oscillation) betweentwo atoms. By properly choosing the collision parameters' values,we have, in particular, created and tested an EPR pair of atoms.Due to the relative insensitivity to the cavity quality factor,the fidelity of this entanglement generation method is compatiblewith Bell's inequalities violation experiments and with thecoherent manipulation of a larger number of atoms. Furthermore, wepresent a new procedure for manufacturing microwave cavities. Withthese cavities, it should in particular become possible to studythe entanglement of the fields confined in two separateresonators.